This is a video I have been wanting to make for some time, in which I discuss what the quaternions are, as mathematical objects, and how we do calculations with them. In particular, we will see how the fundamental equation of the quaternions i^2=j^2=k^2=ijk=-1 easily generates the rule for
From playlist Quaternions
Particle Physics (13 of 41) Elementary Particles: What Is A Quark? (Part 1)
Visit http://ilectureonline.com for more math and science lectures! In this video I will give a detail description of quarks. Next video in the Particle Physics series can be seen at: https://youtu.be/De0U8fUBI7o
From playlist PHYSICS 65 PARTICLE PHYSICS
Quaternions as 4x4 Matrices - Connections to Linear Algebra
In math, it's usually possible to view an object or concept from many different (but equivalent) angles. In this video, we will see that the quaternions may be viewed as 4x4 real-valued matrices of a special form. What is interesting here is that if you know how to multiply matrices, you a
From playlist Quaternions
Animation created for a promo called 3 Times the Prime. Created with Cinema 4D and After Effects.
From playlist KCCI Animations
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From playlist Science Unplugged: Particle Physics
16. Malaria (I): The Case of Italy
Epidemics in Western Society Since 1600 (HIST 234) Of all the diseases studied in this course, malaria has been responsible for the most human suffering. It has evolved alongside humans, and impacted human biology as well as civilization. In the former case, this impact is evident in ge
From playlist Epidemics in Western Society Since 1600 with Frank Snowden
I made this video when I thought I had made a model of the Klein Quartic. But it is wrong, so please ignore it. You can find a corrected version here: https://www.youtube.com/watch?v=ADtwLnxLPTI
From playlist Geometry
Geometric Algebra - Rotors and Quaternions
In this video, we will take note of the even subalgebra of G(3), see that it is isomorphic to the quaternions and, in particular, the set of rotors, themselves in the even subalgebra, correspond to the set of unit quaternions. This brings the entire subject of quaternions under the heading
From playlist Math
Matrix Theory: For the quaternion alpha = 1 - i + j - k, find the norm N(alpha) and alpha^{-1}. Then write alpha as a product of a length and a direction.
From playlist Matrix Theory
quaternion square root of -1. We calculate the square root of -1 using the quaternions, which involves knowing how to multiply quaternion numbers. The answer will surprise you, because it involves spheres and it will make you see complex numbers in a new way, as north and south poles of ba
From playlist Complex Analysis
In this video, I use the coordinate method or Chain Rule method to solve a PDE. It is based on defining clever coordinates and using the Chain Rule to turn the PDE into one that's much easier to solve. Enjoy! Check out my PDE Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmDo
From playlist Partial Differential Equations
We present a solution to question B1 from the 2011 William Lowell Putnam Mathematics Competition. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Putnam Exam Solutions: A1/B1
Calculus AB Homework 3.5 The Chain Rule
Download Packet: https://goo.gl/5At53F ================================= AP Calculus AB / IB Math SL Unit 3: Derivative Rules Lesson 5: The Chain Rule =================================
From playlist AP Calculus AB
Category Theory 1.7: Horizontal Composition and 2-Categories
In this video, I introduce the horizontal composition of natural transformations, the interchange rule, and the basics of 2-Categories/Bicategories. Translate This Video : Notes : None yet Patreon : https://www.patreon.com/user?u=16481182 Teespring : https://teespring.com/stores/fematika
From playlist Category Theory
Closing the Gap: the quest to understand prime numbers - Vicky Neale
Oxford Mathematics Public Lectures: Vicky Neale - Closing the Gap: the quest to understand prime numbers Prime numbers have intrigued, inspired and infuriated mathematicians for millennia and yet mathematicians' difficulty with answering simple questions about them reveals their depth and
From playlist A Vicky Neale Playlist
Distance squared on disk and square
In this video, I answer the following neat question: If you have two points on a circle, then what is on average the distance between them? This problem can be surprisingly (or not) solved using multivariable calculus by converting it into a quadruple (!) integral! Then, I solve the same p
From playlist Double and Triple Integrals
An Exact Formula for the Primes: Willans' Formula
Formulas for the nth prime number actually exist! One was cleverly engineered in 1964 by C. P. Willans. But is it useful? ---------------- References: Herbert Wilf, What is an answer?, The American Mathematical Monthly 89 (1982) 289–292. https://doi.org/10.1080/00029890.1982.11995435 C
From playlist Cool stuff about primes
The Biggest Known Prime Number - Keith Conrad [2018]
Slides for this talk: https://ctnt-summer.math.uconn.edu/wp-content/uploads/sites/1632/2018/05/mersennetalkCTNT.pdf May 29: Keith Conrad (UConn) Title: The Biggest Known Prime Number. Abstract: There are infinitely many primes, but at any moment there is a biggest known prime. Earlier t
From playlist Number Theory
Particle Physics (14 of 41) Elementary Particles: What Is A Quark? (Part 2)
Visit http://ilectureonline.com for more math and science lectures! In this video I will describe the physical aspects of a quark. Next video in the Particle Physics series can be seen at: https://youtu.be/Tokfrq-aJVk
From playlist PHYSICS 65 PARTICLE PHYSICS
The Music of the Primes - Marcus du Sautoy
The Music of the Primes Marcus du Sautoy, Oxford University Thursday, May 8, 2008, at 6:00 pm MIT, Compton Laboratories Building 26, Room 26-100 Access via 60 Vassar Street Marcus du Sautoy, author of the The Music of the Primes, will discuss the mystery of prime numbers, the hi
From playlist Science